Splitting patterns of excellent quadratic forms.
Splitting patterns of excellent quadratic forms.
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优秀二次形式的分裂模式。
DOI：
10.1515/crll.1993.444.183
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
J. Hurrelbrink
中科院分区：
文献类型：
--
作者：
U. Rehmann;J. Hurrelbrink
特征不同于2的域k上的regulär二次型q的分裂模式是基域扩展后可能出现的q的不同Witt指数序列。对于给定的regulär表单q，我们定义了一个称为qextensions的表单类。我们将证明这类的各向异性成员q都有一个只依赖于q的维数和q的分裂模式的分裂模式。这种依赖关系在§2中确定。例如，Pfister形式是这种类型（这里我们有q = 0）；它们的Witt指数要么为0，要么为最大值。对于每一种形式q都有任意高维的^-扩展。带有暗淡q ^ l的^-扩展正是Knebusch引入的“优秀”形式，他在bbbb1,7.11中给出了它们可能的Witt指标的递归公式。一般来说，确定给定二次型的分裂模式似乎是非常困难的，然而，对于优秀的形式，有一种简单的方法来描述它们的分裂模式；这将在§2中讨论。
The Splitting pattern of a regulär quadratic form q over a field k of characteristic different from 2 is the sequence of distinct Witt indices of q which may occur after base field extension. For a given regulär form q we define a elass of forms which we call qextensions. We will show that the anisotropic members q of this class all have a Splitting pattern depending only on the dimension of q and on the Splitting pattern of q. This dependency is determined in § 2. For example, Pfister forms are of this type (here we have q = 0); their Witt index is either 0 or maximal. For every form q there are ^-extensions of arbitrarily high dimension. The ^-extensions with dim q ̂ l are precisely the "excellent" forms introduced by Knebusch, who gave a recursive formula for their possible Witt indices in [3], 7.11. In general, the determination of the Splitting pattern of a given quadratic form seems to be very difficult, however, for excellent forms there is an easy way of describing their Splitting patterns; this will be discussed in §2.